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Is there an approach to solve the following radical equation in $x$?

$(P - 1)x = QR\left( Q + \sigma \sqrt{Q^2 + x} \right)\left( R + sign(P-1) \sigma \sqrt{R^2 + x} \right)$

We know $x\in (0,1)$. We also have $P, Q, R > 0$ and $\sigma \in \{-1,+1\}$.

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    $\begingroup$ It's going to be a bit messy, but what's wrong with good old squaring? $\endgroup$ – Allawonder May 19 at 4:51
  • $\begingroup$ Wolfram alpha solves it. $\endgroup$ – Soumya Basu May 19 at 6:33
  • $\begingroup$ It would. Mostly trusty calculator. $\endgroup$ – Allawonder May 19 at 6:44

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